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IV. Ecosmomics: Independent Complex Network Systems, Computational Programs, Genetic Ecode Scripts

A. A Procreative Ecode: An Ecosmome to Geonome Complementary Hereditary Endowment

Morales, Guillermo and Miguel Munoz. Optimal Input Representation in Neural Systems at the Edge of Chaos. arXiv:2107.05709. University of Granada, Spain complexity theorists (search Munoz) contribute to the latest articulations of nature’s insistent preference for an active balance and poise composed of more or less conserve and create, fixed or flexible, closed or open, modes. Here this optimum occasion is shown to offer much benefit to active informational learning tasks. As such entries typically say nowadays, it is noted that many other physical, biological, cerebral and societal phases are similarly distinguished by this “sweet spot” fittest condition.

Shedding light onto how biological systems represent, process and store information in noisy environments is a key and challenging goal. An innovative hypothesis in the making poses that operating in dynamical regimes near the edge of a phase transition, i.e. at criticality, can provide information-processing living systems with operational advantages as poised between robustness and flexibility. Our contribution in this regard will be to construct an artificial neural network and train it to classify images. Indeed, we find that the best performance is obtained when the network operates near the critical point, at which the eigenspectrum of its covariance matrix follows the same statistics as actual neurons do. Thus, we conclude that operating near criticality can also have the benefit of allowing for flexible, robust and efficient input representations. (Abstract excerpt)

A popular concept from artificial neural networks is that information-processing complex systems, which are composed of many individual interacting units, are best suited to encode, respond, process, and store information if they operate in the dynamical critical point regime of a phase transition, i.e. at the edge between "order" and "disorder.” In regard, there needs to be some trade-off between order and disorder that can be stated in a number of ways, e.g., between "stability and responsiveness" or "robustness and flexibility". The criticality hypothesis poses that such a contrast is resolved near criticality. (1-2)

Muolo, Riccardo, et al. Persistence of Chimera States and the Challenge for Synchronization in Real-World Networks. arXiv:2306.00237. University of Namur, Belgium, University of Limerick and Florida State University provide further theoretical reasons for nature’s broad and deep propensity to seek and reside in this optimum complementary balance.

Orderly phases emerge in nature with synchronization modes as a representative example. In this regard, the role played by interactions between the constituting parts of a complex system is a prime research subject bridging network science and dynamic phenomena. An especial interest is the presence of chimera states whereby synchronized oscillations coexist with asynchronous ones. Such alternate states of coherence and incoherence exemplify how order and disorder can coexist over a long time. Our concern is their presence in real-world networks. By way of a symmetry-breaking mechanism, we describe how non-normality, a ubiquitous structural property, can cause this bilateral occasion. (Excerpt)

Nettuno, Beatrice, et al. The role of mobility in epidemics near criticality. arXiv:2402.06505. Four years into the pandemic, a team of biophysicists at Ludwig-Maximilians-University including Erwin Frey achieve a host sophisticated mathematical formulation which draws upon and widely applies both physical principles and complexity science. Renormalization group theory and self-organized phase transitions are found to independently underline and channel this dynamic public malady wherever it occurs.

The general epidemic process (GEP) describes its spread within a population of susceptible individuals. We investigate the impact of mobility on disease spreading threshold by two generalizations of GEP, where the mobility of susceptible and recovered individuals is examined independently. The critical dynamics are studied through a perturbative renormalization group approach and large-scale stochastic simulations. This analysis predicts that both models belong to the same universality class which describe the critical epidemic dynamics. At the associated renormalization group fixed point, the immobile species decouples from the dynamics of the infected species due to coupling with the diffusive species.. Numerical simulations in two dimensions affirm our renormalization group results by identifying the same set of critical exponents for both models. (Excerpt)

Notarmuzi, Daniele, et al. Universality, Criticality and Complexity of Information Propagation in Social Media. arXiv:2109.00116. Indiana University systems theorists including Filippo Radicchi post a strong exposition to date of how all manner of dynamic self-organizing systems can be seen to spring from and express an iconic array of similar forms and behaviors. As a result, it is noted that all this disparate phenomena quite implies an independent generative source which seems to be in eternal effect. Into these 2020s, a natural propensity to seek and reside at an active bilateral poise from galaxies to Google becomes evident. For later work by this group see Critical avalanches of Susceptible-Infected-Susceptible dynamics in finite networks at 2301.06939.

Information avalanches in social media are typically studied in a similar fashion as avalanches of neuronal activity in the brain. Whereas much literature reveals a substantial agreement about a unique process that characterizes neuronal activity across organisms, the dynamics of information in online social media is far less understood. Here, we analyze almost 1 billion time-stamped events collected from a multitude of platforms (Telegram, Twitter and Weibo) over some 10 years to show that the propagation of information in social media is a universal and critical process. Universality arises from the observation of identical macroscopic patterns, irrespective of the specific system. Critical behavior is deduced from the power-law distributions, and their hyperscaling relations, which control the size and duration of avalanches of information. (Abstract excerpt)

For example, there is large agreement on the fact that neuronal activity in the brain is universal and critical. Universality is the notion that nearly identical avalanche statistics are observed for a multitude of organisms. Criticality instead refers to the fact that avalanche statistics are characterized by algebraic distributions. (4)

We speculate that our results extend beyond the six platforms considered here. If so, there must be a mechanism that explains the universality shown by the data, involving a critical dynamics that is independent of the peculiarities implemented in the individual platforms. Understanding where this mechanism is rooted in and how to exploit it for the prediction of the propagation of information in online social media remain open challenges for future research. (10)

Ohler, Simon, et al. Towards Learning Self-Organized Criticality of Rydberg Atoms using Graph Neural Networks. arXiv:2207.08927. University of Kaiserslautern, Germany and Merantix Momentum, AI Campus, Berlin researchers including Johannes Otterbach at once testify to nature’s universal preference for this optimum state and describe an avail of deep machine algorithmic methods by which to advance their latest studies.

Self-Organized Criticality (SOC) is a ubiquitous dynamical phenomenon believed to be responsible for the emergence of universal scale-invariant behavior in many disparate systems such as forest fires, viral epidemics or atomic excitation. SOC is found across large-scale and long-range spatio-temporal correlations as a result of local interactions. We investigate Graph Neural Networks (GNNs) as an effective way to model a physical system of driven Rydberg atoms as a typical SOC occasion. While inspired by active Rydberg atoms, the approach could readily be applied to many other cases. (Abstract excerpt)

Deep Learning methods deliver impact for many applications ranging from Computer Vision, Natural Language, Processing, Audio and Speech Processing to Optimal Control. In recent years we also see these methods drive innovation in areas of scientific interest, such as drug discovery, protein folding, molecule dynamics, as well as classic multi-particle systems and many more. In the context of particle dynamics the class of Graph Neural Networks (GNNs) are particularly successful. We build up on this success and investigate the application of GNNs to learn the time-evolution of a complex many-body system in the regime of so-called self-organized criticality (SOC). (1)

A Rydberg atom is an excited atom with one or more electrons that have a very high principal quantum number. The higher the value of n, the farther the electron is from the nucleus, on average. Rydberg atoms have certain properties including a response to electric and magnetic fields, long decay periods and electron wavefunctions.

Okur, Zeynep, et al. Control of neuronal excitation–inhibition balance by BMP–SMAD1 signalling. Nature. April 17, 2024. University of Basel, Basel and Swiss Institute of Bioinformatics, Basel neuro-researchers describe further findings that constant cerebral processes do indeed reside at a best dynamic balance of less or more stimulation. Once again, in every phenomenal way it seems, nature seeks and prefers this optimum reciprocity.


Throughout life, neuronal networks in the mammalian neocortex maintain a balance of excitation and inhibition states that are essential for neuronal computation. To maintain this poise, microcircuits composed of excitatory and inhibitory neurons adjust their connectivity and function. Here we study a signal pathway in the adult mouse neocortex where overactive neurons are sent to the network by higher levels of BMP2, a growth factor. Ultimately, this impairment of the functional recruitment of PV interneurons disrupts the cortical excitation–inhibition balance, with mice exhibiting seizures. Our findings suggest that developmental morphogen signalling is repurposed to stabilize cortical networks in the adult mammalian brain.
Despite a wide range of sensory stimulus, cortical circuits exhibit stable activity patterns that enable optimal information coding by the network. These adaptations happen from near instantaneous adjustments of excitation and inhibition during sensory processing, to slower modifications of synaptic connectivity. Thus, both rapid cell-intrinsic and long-lasting transcellular signalling processes have evolved to ensure the function and stability of the cortical network. (6)

Ortez, Ronaldo and John Rundle. Correlated Avalanche-Burst Invasion Percolation: Multifractal Origins of a Characteristic Self-Organized Critical System.. arXiv:2303.10272. UC Davis system physicists continue to deftly tease out another presence of a consistent, self-similar dynamic balance as a deep distinction of nature’s optimum preference.

We extend our previous avalanche-burst invasion percolation (AIP) model by adding long-range correlations between sites described by fractional Brownian statistics. In this way, we are able to produce a family of critical exponents characterized by the local long-range correlations inherent to host sediment. As a result, we show how multiple cluster scaling power laws gives rise to a truly multifractal system. (Excerpt)

Pereverzev, Sergey. Dark Matter Searches and Energy Accumulation and Release in Materials. arXiv:2212.13964. This presentation at the 14th International Conference on Identification of Dark Matter (Vienna 2022) by a Lawrence Livermore experimental physicist describes highly complex, diverse experiments which show how self-organized critical phenomena is inherently pervasive all manner of material and energetic phases.

This presentation at the 14th International Conference on Identification of Dark Matter (Vienna 2022) by a Lawrence Livermore experimental physicist describes highly complex, diverse experiments which show how self-organized critical phenomena is inherently pervasive all manner of material and energetic phases.

Provata, Astero.. From Turing Patterns to Chimera States in the 2D Brusselator Model. arXiv:2212.01297. A National Center for Scientific Research, Athens (bio below) physicist contributes a latest explanation about these spatial and temporal conditions which appear across a widening array of life’s natural and social phenomena. A novel contribution is their aptness to shift from a morphogenetic phase to a self-organized critical activity. On a personal note, I had lunch with Ilya Prigogine in a group in 1987 at a conference. Some 35 years on, into these 2020s the complexity sciences have come to and settled on this common non-equilibrium occasion, a true universality in kind.

The Brusselator has been used as a prototype model for autocatalytic reactions, and for the Belouzov-Zhabotinsky reaction. When coupled at the diffusive limit, the it undergoes a bifurcation resulting in the formation of classical Turing patterns such as spots, stripes and spirals. In the present study we use generic nonlocally coupled Brusselators and show that in the diffuse limit of the coupling range, the Turing effects are recovered, while for intermediate coupling ranges and appropriate parameter values chimera states are produced. This study demonstrates how the parameters of a typical nonlinear oscillator can be tuned so that the coupled system passes from spatially stable structures to dynamical spatiotemporal chimera modes. (Abstract)

A decade after the first theoretical prediction of chimera states, experimental evidence has been reported in mechanical, physical and chemical lsystems consisting of interacting oscillatory units. Some examples are optical systems, in electronic circuits, in mechanics, in biomedicine, and reaction diffusion systems. Beyond experimental findings in the laboratory, chimera states have been associated with the uni-hemispheric sleep in mammals and birds, with the onset of epileptic seizures and other biomedical conditions. (2)
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The Brusselator is a theoretical model for a type of autocatalytic reaction. It was proposed by Ilya Prigogine and collaborators at the Université Libre de Bruxelle A Belousov–Zhabotinsky reaction servse as a classic example of non-equilibrium thermodynamics, resulting in the establishment of a nonlinear chemical oscillator.

Astero Provata received her B.Sc. degree in physics from the University of Athens in 1985 and Ph.D. degree from Boston University, USA, in 1991. She is currently Research Director of Nanoscience and Nanotechnology, Greece. Her interests include neural networks, nonlinear dynamical systems, statistical physics, fractals, and complex systems.

Proverbio, Daniele, et al. Buffering in Cell Regulation Motifs Close to Criticality. arXiv:2212.08600. As late 2022 scientific studies proceed to find a widening propensity across life’s metabolic, and cerebral phases to achieve and benefit from dynamic sensitivities, University of Luxembourg theorists show how these a these nuanced responses can also foster a ecological resilience.

Bistable biological regulatory systems need to cope with stochastic noise to fine-tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to demonstrate that cooperative interactions buffer noise-induced regime shifts. Our generic framework, based on minimal models, can be used to extract robustness and variability properties of more complex models and empirical data close to criticality. (Abstract)

Overall, our study characterised fundamental dynamical mechanisms to buffer systems’ variability in critical regimes. We determined parameter ranges, corresponding to plausible cooperativity values for the positive feedback loop motif, where both variance and autocorrelation display low relative sensitivity to additive noise. (5)

Rao, Ankit, et al. Self-Assembled Meuromorphic Networks at Self-Organized Criticality in Ag-hBN Platform. arXiv:2301.01619. Eight India Institute of Science and University of Groningen researchers describe an involved physical material method by which to attain, demonstrate and explain this optimum performance condition.

Networks and systems which exhibit brain-like behavior can analyze information from noisy data with low power consumption due to the critical nature and complex interconnectivity of their neuronal-like network. We show that a system comprised of hexagonal Boron Nitride (hBN) films contacted with Silver (Ag), that can uniquely host two different self-assembled networks, which are self-organized at criticality (SOC). This system shows bipolar resistive switching between high resistance (HRS) and low resistance states (LRS). The temporal avalanche dynamics in both these states exhibit power-law scaling,
The temporal avalanche dynamics in both these states exhibit power-law scaling, long-range temporal correlation, and SOC. (Abstract excerpt)

Rispoli, Matthew, et al. Quantum Critical Behavior at the Many-Body Localization Transition. arXiv:1812.06959. We cite this 2018 entry by Harvard physicists in Spring 2023 as an example of how some five years later their early witness of this phenomenal behavior has become robustly evident, as this section documents. As the PediaPedia Earthica section next continues, as the spiral of science to a global sapiensphere with her/his own findings and knowledge, the present moment and advance can be appreciated as convergent synthesis and discovery.

Phase transitions are driven by collective fluctuations of a system's constituents that emerge at a critical point. This mechanism has been extensively explored for classical and quantum systems in equilibrium, whose critical behavior is described by a general theory of phase transitions. Our results unify the system's microscopic structure with its macroscopic quantum critical behavior, and they provide an essential step towards understanding criticality and universality in non-equilibrium systems. (Excerpt)

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